Two normal distributions with equal means but different standard deviations.
Two distribution curves with identical means but different variabilities. The curve with the greater variability (green) yields higher values in both the lowest and highest ends of the range.

The variability hypothesis, also known as the greater male variability hypothesis, is the hypothesis that males generally display greater variability in traits than females do.

It has often been discussed in relation to human cognitive ability, where some studies appear to show that males are more likely than females to have either very high or very low IQ test scores. In this context, there is controversy over whether such sex-based differences in the variability of intelligence exist, and if so, whether they are caused by genetic differences, environmental conditioning, or a mixture of both.

Sex-differences in variability have been observed in many abilities and traits – including physical, psychological and genetic ones – across a wide range of sexually dimorphic species. On the genetic level, the greated phenotype variability in males is likely to be associated with human males being a heterogametic gender, while females are homogametic and thus are more likely to diplay averaged traits in their phenotype.[1]


The notion of greater male variability—at least in respect to physical characteristics—can be traced back to the writings of Charles Darwin.[2] When he expounded his theory of sexual selection in The Descent of Man and Selection in Relation to Sex, Darwin cites some observations made by his contemporaries. For example, he highlights findings from the Novara Expedition of 1861–1867 where "a vast number of measurements of various parts of the body in different races were made, and the men were found in almost every case to present a greater range of variation than the women" (p. 275). To Darwin, the evidence from the medical community at the time, which suggested a greater prevalence of physical abnormalities among men than women, was also indicative of men's greater physical variability.

Although Darwin was curious about sex differences in variability throughout the animal kingdom, variability in humans was not a chief concern of his research. The first scholar to carry out a detailed empirical investigation on the question of human sex differences in variability in both physical and mental faculties, was the sexologist Havelock Ellis. In his 1894 publication Man and Woman: A Study of Human Secondary Sexual Characters, Ellis dedicated an entire chapter to the subject, entitled "The Variational Tendency of Men".[3] In this chapter he posits that "both the physical and mental characters of men show wider limits of variation than do the physical and mental characters of women" (p. 358). Ellis documents several studies that support this assertion (see pp. 360–367), and

"By the 1890s several studies had been conducted to demonstrate that variability was indeed more characteristic of males...The biological evidence overwhelmingly favored males as the more variable sex."[4]

Early controversies in the 20th century

The publication of Ellis's Man and Woman led to an intellectual dispute about the variability hypothesis between Ellis and the statistician Karl Pearson, whose critique of Ellis's work was both theoretical and methodological. After Pearson dismissed Ellis's conclusions, he then "presented his own data to show that it was the female who was more variable than the male"[4] Ellis wrote a letter to Pearson thanking him for the criticisms which would allow him to present his arguments "more clearly & precisely than before", but did not yield his position regarding greater male variability.[4]

Support for the greater male variability hypothesis grew during the early part of the 20th century.[2] During this period, the attention of researchers shifted towards studying variability in mental abilities partly due to the advent of standardised mental tests (see the history of the Intelligence quotient), which made it possible to examine intelligence with greater objectivity and precision.

One advocate of greater male variability during this time was the American psychologist Edward Thorndike, one of the leading exponents of mental testing who played an instrumental role in the development of today's Armed Services Vocational Aptitude Battery ASVAB. In his 1906 publication Sex in Education, Thorndike argued that while mean level sex differences in intellectual ability appeared to be negligible, sex differences in variability were clear.[2] Other influential proponents of the hypothesis at this time were psychologists G. Stanley Hall and James McKeen Cattell.[5][6][7] Thorndike believed that variability in intelligence could have a biological basis and suggested that this could have important implications for achievement and pedagogy. For example, he postulated that greater male variation could mean "eminence and leadership of the world's affairs of whatever sort will inevitably belong oftener to men."[8] In addition, since the number of women that fall within the extreme top-end of the intelligence distribution would be inherently smaller, he suggested that educational resources should be invested in preparing women for roles and occupations that require only a mediocre level of cognitive ability.[9]

Leta Hollingworth's studies

See also: Leta Hollingworth

By examining the case records of 1,000 patients at the Clearing House for Mental Defectives, Leta Hollingworth determined that, although men outnumbered women in the clearing house, the ratio of men to women decreased with age. Hollingworth explained this to be the result of men facing greater societal expectations than women. Consequently, deficiencies in men were often detected at an earlier age, while similar deficiencies in women might not be detected because less was expected of them. Therefore, deficiencies in women would be required to be more pronounced than those in men in order to be detected at similar ages.[5][6][9][10][7]

Hollingworth also attacked the variability hypothesis theoretically, criticizing the underlying logic of the hypothesis.[5][6][9][11] Hollingworth argued that the variability hypothesis was flawed because: (1) it had not been empirically established that men were more anatomically variable than women, (2) even if greater anatomical variability in men were established this would not necessarily mean that men were also more variable in mental traits, (3) even if it were established that men were more variable in mental traits this would not automatically mean that men were innately more variable, (4) variability is not significant in and of itself, but rather depends on what the variability consists of, and (5) that any possible differences in variability between men and women must also be understood with reference to the fact that women lack the opportunity to achieve eminence because of their prescribed societal and cultural roles.[5][6][9] Additionally, the argument that great variability automatically meant greater range was criticized by Hollingworth.[9][12][how?]

In an attempt to examine the validity of the variability hypothesis, while avoiding intervening social and cultural factors, Hollingworth gathered data on birth weight and length of 1,000 male and 1,000 female newborns. This research found virtually no difference in the variability of male and female infants, and it was concluded that if variability "favoured" any sex it was the female sex.[5][6][9][10] Additionally, along with the anthropologist Robert Lowie, Hollingworth published a review of literature from anatomical, physiological, and cross-cultural studies, in which no objective evidence was found to support the idea of innate female inferiority.[5][6][9][12][11]

Modern studies

The 21st century has witnessed a resurgence of research on gender differences in variability, with most of the emphasis on humans. The results vary based on the type of problem, but some recent studies have found that the variability hypothesis is true for parts of IQ tests, with more men falling at the extremes of the distribution.[13][14] Publications differ as to the extent and distribution of male variability, including on whether variability can be shown across various cultural and social factors.[15][16]

A 2007 meta-analysis found that males are more variable on most measures of quantitative and visuospatial ability, making no conclusions of its causation.[17]

A 2008 analysis of test scores across 41 countries published in Science concluded that "data shows a higher variance in boys' than girls' results on mathematics and reading tests in most OECD countries", the results implying that "gender differences in the variance of test scores are an international phenomenon". However, it also found that several countries failed to exhibit a gender difference in variance.[13]

A 2008 study reviewed the history of the hypothesis that general intelligence is more biologically variable in males than in females and presented data which the authors claim "in many ways are the most complete that have ever been compiled [and which] substantially support the hypothesis".[2]

A 2009 study in developmental psychology examined non-cognitive traits including blood parameters and birth weight as well as certain cognitive traits, and concluded that "greater intrasex phenotype variability in males than in females is a fundamental aspect of the gender differences in humans".[18]

Recent studies indicate that greater male variability in mathematics persists in the U.S., although the ratio of boys to girls at the top end of the distribution is reversed in Asian Americans.[19] A 2010 meta-analysis of 242 studies found that males have an 8% greater variance in mathematical abilities than females, which the authors indicate is not meaningfully different from an equal variance. Additionally, they find several datasets indicate no or a reversed variance ratio.[20]

A 2014 review found that males tend to have higher variance on mathematical and verbal abilities but females tend to have higher variance on fear and emotionality; however, the differences in variance are small and without much practical significance and the causes remain unknown.[21] A 2005 meta-analyses found greater female variability on the standard Raven's Progressive Matrices, and no difference in variability on the advanced progressive matrices, but also found that males had a higher average general intelligence.[22] This meta analysis, however, was criticized for bias by the authors and for poor methodology.[23][24][25]

A 2016 study by Baye and Monseur examining twelve databases from the International Association for the Evaluation of Educational Achievement and the Program for International Student Assessment, were used to analyse gender differences within an international perspective from 1995 to 2015, and concluded, "The 'greater male variability hypothesis' is confirmed."[26] This study found that on average, boys showed 14% greater variance than girls in science, reading, and math test scores. In reading, boys were significantly represented at the bottom of score distribution, whereas for maths and science they featured more at the top.

The results of Baye and Monseur have been both replicated and criticized in a 2019 meta-analytical extension published by Helen Gray and her associates, which broadly confirmed that variability is greater for males internationally but that there is significant heterogeneity between countries. They also found that policies leading to greater female participation in the workforce tended to increase female variability and, therefore, decrease the variability gap. They also point out that Baye and Monseur had themselves observed a lack of international consistency, leading more support to a cultural hypothesis.[27]

A 2018 meta analysis of over 1 million school-aged children found strong evidence for higher variability in boys' grades, but for girls to receive higher grades on average, both of which the authors describe as "in line with previous studies". Due in part to the combination of these factors, they conclude that differences in variability are insufficient to explain disparities in STEM college admissions. They note: "Simulations of these differences suggest the top 10% of a class contains equal numbers of girls and boys in STEM, but more girls in non-STEM subjects."[28]

In October 2020, with respect to brain morphometry, researchers reported "the largest-ever mega-analysis of sex differences in variability of brain structure"; they stated that they "observed significant patterns of greater male than female between-subject variance for all subcortical volumetric measures, all cortical surface area measures, and 60% of cortical thickness measures. This pattern was stable across the lifespan for 50% of the subcortical structures, 70% of the regional area measures, and nearly all regions for thickness." The authors emphasize, however, that this has of yet no practical interpretive meaning, says nothing on causation, and requires further examination and replication.[29]

A 2020 study in birds found that male mountain chickadees exhibit larger variation in reversal learning performance compared with females.[30] It's noteworthy that in birds the heterogametic sex is the female, that is the individuals of a species in which the sex chromosomes are not the same. Although just one study, this seems to disqualify that being the heterogametic sex could be a cause for male variability.

In 2021, two meta-analyses on preference measurement in experimental economics find strong evidence for greater male variability for cooperation (variance ratio: 1.30, 95% CI [1.22, 1.38]),[31] time preferences (1.15, [1.08, 1.22]), risk preferences (1.25 [1.13, 1.37]), dictator game offers (1.18 [1.12, 1.25]) and transfers in the trust game (1.28 [1.18, 1.39]).[32]

A 2021 review investigating different hypotheses behind the discrepancy of sexes in STEM jobs summarizes the greater variability research with respect to this question. Given that research finds greater variability in males with in quantitative and nonverbal reasoning,[33] they hold that this can explain some, but not all of the difference seen in STEM occupations.[34] With regard to the question of whether these results are due to societal influences or of biological origins, they hold that the results showing greater variance at a very young age (for instance IQ differences in variability between the sexes is visible from a young age on [35]) lend credence to the theory that biological factors might explain a large part of the observed data.

A 2022 analysis of a large database on energy expenditure in adult humans found that "even when statistically comparing males and females of the same age, height, and body composition, there is much more variation in total, activity, and basal energy expenditure among males".[36]

Contemporary controversies

The variability hypothesis has continued to spur controversy within academic circles.

In a 1992 paper titled "Variability: A Pernicious Hypothesis," Stanford Professor Nel Noddings discussed the social history which she argued explains "the revulsion with which many feminists react to the variability hypothesis."[37]

One of the most prominent incidents occurred in 2005 when then Harvard President, Larry Summers, addressed the National Bureau of Economic Research Conference on the subject of gender diversity in the science and engineering professions, saying: "It does appear that on many, many different human attributes—height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability—there is relatively clear evidence that whatever the difference in means—which can be debated—there is a difference in the standard deviation, and variability of a male and a female population."[38][39] His remarks caused a backlash; Summers faced a no-confidence vote from the Harvard faculty, prompting his resignation as President.[40][41]

In a similar incident in 2017, Google software engineer James Damore was fired immediately after posting an internal memo on diversity (see Google's Ideological Echo Chamber) suggesting possible innate biological factors including greater male variability to help explain the underrepresentation of women in hi-tech jobs.[42]

That same year, a mathematics research paper presenting a possible evolutionary explanation for the variability hypothesis was peer-reviewed, accepted, and formally published in The New York Journal of Mathematics. Three days later, that article was removed without explanation and replaced by an unrelated article by different authors. This caused debate within the scientific community and international publicity.[43][44][45] A revised version was subsequently peer reviewed again and published in the Journal of Interdisciplinary Mathematics.[46]

See also


  1. ^
  2. ^ a b c d Johnson, Wendy; Carothers, Andrew; Deary, Ian J. (November 2008). "Sex Differences in Variability in General Intelligence: A New Look at the Old Question". Perspectives on Psychological Science. 3 (6): 518–531. CiteSeerX doi:10.1111/j.1745-6924.2008.00096.x. PMID 26158978. S2CID 22884415.
  3. ^ Ellis, H. (1894). Man and Woman: A Study of Human Secondary Sexual Characters (1st ed.). London: Walter Scott. Retrieved 15 March 2019.
  4. ^ a b c Shields, S. (1982). "The variability hypothesis: The history of a biological model of sex differences in intelligence". Signs. 7 (4): 769–797. doi:10.1086/493921. JSTOR 3173639. S2CID 143951248.
  5. ^ a b c d e f Benjamin, Ludy T (1975). "The pioneering work of Leta Hollingworth in the psychology of women" (PDF). Nebraska History. 56 (4): 457–575. Archived from the original on May 22, 2013.((cite journal)): CS1 maint: unfit URL (link)
  6. ^ a b c d e f Benjamin, Ludy T. (March 1990). "Leta Stetter Hollingworth: Psychologist, educator, feminist". Roeper Review. 12 (3): 145–151. doi:10.1080/02783199009553259.
  7. ^ a b Shields, Stephanie A. (2013). "Leta Stetter Hollingworth: 'Literature of Opinion' and the Study of Individual Differences". In Kimble, Gregory A.; Wertheimer, Michael; White, Charlotte (eds.). Portraits of Pioneers in Psychology. Psychology Press. pp. 243–255. ISBN 978-1-317-75992-8.
  8. ^ Hollingworth, L. S. (1914). "Variability as related to sex differences in achievement: A critique". American Journal of Sociology. 19 (4): 510–530. doi:10.1086/212287.
  9. ^ a b c d e f g Shields, Stephanie A. (1975). "Ms. Pilgrim's progress: The contributions of Leta Stetter Hollingworth to the psychology of women". American Psychologist. 30 (8): 852–857. doi:10.1037/h0077024.
  10. ^ a b Benjamin, L. T., & Shields, S. A. (1990). "Leta Stetter Hollingworth (1886–1939)." In A. N. O’Connell & N. F. Russo (Eds.), Women in Psychology: A Bio-Bibliographic Sourcebook (pp.173–183). Westport, Connecticut: Greenwood.
  11. ^ a b Poffenberger, A. T. (1940). "Leta Stetter Hollingworth: 1886–1939". The American Journal of Psychology. 53 (2): 299–301. JSTOR 1417431. ProQuest 1289796105.
  12. ^ a b Denmark, F. L., & Fernandez, L. C. (1993). "Historical development of the psychology of women." In F. L. Denmark & M. A. Paludi (Eds.), Psychology of Women: A Handbook of Issues and Theories (pp. 1–22). Westport, Connecticut: Greenwood.
  13. ^ a b Machin, S.; Pekkarinen, T. (28 November 2008). "ASSESSMENT: Global Sex Differences in Test Score Variability". Science. 322 (5906): 1331–1332. doi:10.1126/science.1162573. PMID 19039123. S2CID 38847707.
  14. ^ Hedges, L.; Nowell, A (7 July 1995). "Sex differences in mental test scores, variability, and numbers of high-scoring individuals". Science. 269 (5220): 41–45. Bibcode:1995Sci...269...41H. doi:10.1126/science.7604277. PMID 7604277. S2CID 15312296.
  15. ^ Feingold, Alan (January 1994). "Gender differences in variability in intellectual abilities: A cross-cultural perspective". Sex Roles. 30 (1–2): 81–92. doi:10.1007/BF01420741. S2CID 144659213.
  16. ^ Hyde, Janet S.; Mertz, Janet E. (2 June 2009). "Gender, culture, and mathematics performance". Proceedings of the National Academy of Sciences. 106 (22): 8801–8807. Bibcode:2009PNAS..106.8801H. doi:10.1073/pnas.0901265106. PMC 2689999. PMID 19487665.
  17. ^ Halpern, Diane F.; Benbow, Camilla P.; Geary, David C.; Gur, Ruben C.; Hyde, Janet Shibley; Gernsbacher, Morton Ann (August 2007). "The Science of Sex Differences in Science and Mathematics". Psychological Science in the Public Interest. 8 (1): 1–51. doi:10.1111/j.1529-1006.2007.00032.x. PMC 4270278. PMID 25530726.
  18. ^ Lehre, Anne‐Catherine; Lehre, Knut; Laake, Petter; Danbolt, Niels (2009). "Greater intrasex phenotype variability in males than in females is a fundamental aspect of the gender differences in humans". Developmental Psychobiology. 51 (2): 198–206. doi:10.1002/dev.20358. PMID 19031491. S2CID 21802694.
  19. ^ Hyde, J. S.; Lindberg, S. M.; Linn, M. C.; Ellis, A. B.; Williams, C. C. (25 July 2008). "Gender Similarities Characterize Math Performance". Science. 321 (5888): 494–495. doi:10.1126/science.1160364. PMID 18653867. S2CID 28135226.
  20. ^ Lindberg, Sara M.; Hyde, Janet Shibley; Petersen, Jennifer L.; Linn, Marcia C. (2010). "New trends in gender and mathematics performance: A meta-analysis". Psychological Bulletin. 136 (6): 1123–1135. doi:10.1037/a0021276. PMC 3057475. PMID 21038941.
  21. ^ Hyde, Janet Shibley (3 January 2014). "Gender Similarities and Differences". Annual Review of Psychology. 65 (1): 373–398. doi:10.1146/annurev-psych-010213-115057. PMID 23808917. S2CID 30544410.
  22. ^ Irwing, Paul; Lynn, Richard (November 2005). "Sex differences in means and variability on the progressive matrices in university students: A meta-analysis". British Journal of Psychology. 96 (4): 505–524. doi:10.1348/000712605X53542. PMID 16248939. S2CID 14005582.
  23. ^ Blinkhorn, Steve (November 2005). "A gender bender". Nature. 438 (7064): 31–32. doi:10.1038/438031a. PMID 16267535. S2CID 3181219.
  24. ^ Blinkhorn, Steve (July 2006). "Is there a sex difference in IQ scores? (Reply)". Nature. 442 (7098): E1–E2. doi:10.1038/nature04967. PMID 16888850. S2CID 148898739.
  25. ^ McKie, Robin (6 November 2005). "Battle of the sexes: Who has the bigger brain?". The Guardian.
  26. ^ Baye, Ariane; Monseur, Christian (2016). "Gender differences in variability and extreme scores in an international context". Large-Scale Assessments in Education. 4 (4): 1–16. doi:10.1186/s40536-015-0015-x. hdl:20.500.12799/3831.
  27. ^ Gray, Helen; Lyth, Andrew; McKenna, Catherine; Stothard, Susan; Tymms, Peter; Copping, Lee (December 2019). "Sex differences in variability across nations in reading, mathematics and science: a meta-analytic extension of Baye and Monseur (2016)". Large-Scale Assessments in Education. 7 (1). doi:10.1186/s40536-019-0070-9. ProQuest 2178957909.
  28. ^ O’Dea, R. E.; Lagisz, M.; Jennions, M. D.; Nakagawa, S. (25 September 2018). "Gender differences in individual variation in academic grades fail to fit expected patterns for STEM". Nature Communications. 9 (1): 3777. Bibcode:2018NatCo...9.3777O. doi:10.1038/s41467-018-06292-0. PMC 6156605. PMID 30254267.
  29. ^ Wierenga, Lara M.; Doucet, Gaelle E.; Dima, Danai; et al. (2020). "Greater male than female variability in regional brain structure across the lifespan". Human Brain Mapping. 43 (1): 470–499. doi:10.1002/hbm.25204. PMC 8675415. PMID 33044802.
  30. ^ Branch, Carrie L.; Sonnenberg, Benjamin R.; Pitera, Angela M.; Benedict, Lauren M.; Kozlovsky, Dovid Y.; Bridge, Eli S.; Pravosudov, Vladimir V. (29 July 2020). "Testing the greater male variability phenomenon: male mountain chickadees exhibit larger variation in reversal learning performance compared with females". Proceedings. Biological Sciences. 287 (1931): 20200895. doi:10.1098/rspb.2020.0895. ISSN 1471-2954. PMC 7423667. PMID 32673560.
  31. ^ Thöni, Christian; Volk, Stefan; Cortina, Jose M. (January 2021). "Greater Male Variability in Cooperation: Meta-Analytic Evidence for an Evolutionary Perspective". Psychological Science. 32 (1): 50–63. doi:10.1177/0956797620956632. ISSN 0956-7976. PMID 33301379. S2CID 228101677.
  32. ^ Thöni, Christian; Volk, Stefan (2021-06-08). "Converging evidence for greater male variability in time, risk, and social preferences". Proceedings of the National Academy of Sciences. 118 (23): e2026112118. Bibcode:2021PNAS..11826112T. doi:10.1073/pnas.2026112118. ISSN 0027-8424. PMC 8201935. PMID 34088838.
  33. ^ Strand, Steve; Deary, Ian J.; Smith, Pauline (2006). "Sex differences in Cognitive Abilities Test scores: A UK national picture". British Journal of Educational Psychology. 76 (3): 463–480. doi:10.1348/000709905X50906. ISSN 2044-8279. Retrieved 2023-04-25.
  34. ^ Stewart-Williams, Steve; Halsey, Lewis G (2021-01-01). "Men, women and STEM: Why the differences and what should be done?". European Journal of Personality. 35 (1): 3–39. doi:10.1177/0890207020962326. ISSN 0890-2070.
  35. ^ Arden, Rosalind; Plomin, Robert (2006-07-01). "Sex differences in variance of intelligence across childhood". Personality and Individual Differences. 41 (1): 39–48. doi:10.1016/j.paid.2005.11.027. ISSN 0191-8869. Retrieved 2023-04-25.
  36. ^ Halsey, Lewis G.; Careau, Vincent; Pontzer, Herman; et al. (October 2022). "Variability in energy expenditure is much greater in males than females". Journal of Human Evolution. 171. doi:10.1016/j.jhevol.2022.103229. hdl:10138/352714.
  37. ^ Noddings, Nel (Spring 1992). "Variability: A Pernicious Hypothesis". Review of Educational Research. 62 (1): 85–88. doi:10.3102/00346543062001085.
  38. ^ "Full Transcript: President Summers' Remarks at the National Bureau of Economic Research, Jan. 14 2005". The Harvard Crimson. Retrieved 2 July 2019.
  39. ^ Jaschik, Scott (18 February 2005). "What Larry Summers Said". Inside Higher Ed.
  40. ^ Finder, Alan; Healy, Patrick D.; Zernike, Kate (22 February 2006). "President of Harvard Resigns, Ending Stormy 5-Year Tenure". The New York Times. Archived from the original on 22 March 2017.
  41. ^ Daniel Golden and Steve Stecklow (22 February 2006). "Facing War With His Faculty, Harvard's Summers Resigns".
  42. ^ Sean Stevens and Jonathan Haidt (4 September 2017). "The Greater Male Variability Hypothesis – An Addendum to our post on the Google Memo 2017".
  43. ^ Azvolinsky, Anna (27 September 2018). "A Twice-Retracted Paper on Sex Differences Ignites Debate". The Scientist. Retrieved 2018-11-03.
  44. ^ "What really happened when two mathematicians tried to publish a paper on gender differences? The tale of the emails". Retraction Watch. 17 September 2018. Retrieved 2023-01-30.
  45. ^ Neumann, Marc (18 September 2018). "Kann Mathematik sexistisch sein? Ein Aufsatz über Intelligenzverteilung unter Männern und Frauen wurde in den USA jedenfalls zensuriert". Neue Zürchner Zeitung. Retrieved 2023-01-30.
  46. ^ Hill, Theodore P. (2020-07-03). "Modeling the evolution of differences in variability between sexes". Journal of Interdisciplinary Mathematics. 23 (5): 1009–1031. doi:10.1080/09720502.2020.1769827. ISSN 0972-0502.